I'm looking at the first 100,000 digits of pi. Lo and behold, 00000 shows up once. So does 11111. What are the odds of each of those happening? It's 1:100,000!

Absolutely astonishing.

As an aside, the inevitability of weird flukes in large sample sizes really sinks in if you've ever wasted part of a year multi-tabling online poker. You'll see some hands play out in totally WTF fashion, as 1:100 and 1:1,000 probabilities come good.

The lesson, of course, is that when you play thousands of hands, encountering such oddities with your money at stake is no longer nearly impossible. It's moved into the zone of nearly certain.